Theorem REF  contains as a special case the main result of [1]}: when \(n=1\)  and \(\phi \in V_{g,1}\)  is a suitable perturbation of the canonical stability condition (which is then general), \(\overline{\mathcal {J}}_{g,1}(\phi )\)  is isomorphic (up to \(\operatorname{\mathbb {G}_m}\) -rigidification) to the Esteves' compactified universal Jacobian stack \(\overline{\mathcal {J}}_{\phi ,g}\)  of loc. cit. (see Remark REF  below) and so Theorem REF  states that the non-Archimedean skeleton of Esteves' compactified universal Jacobian \(\overline{\mathcal {J}}_{\phi ,g}\)  can be identified with \(\overline{J}^{trop}_{g,1}(\phi )\)  (which can be shown to be isomorphic to the generalized extended cone complex \(\overline{J}^{trop}_{\phi ,g}\)  constructed in loc. cit.) making the natural diagram of tropicalization maps commute, which is exactly [1]}However, it seems to us that [1]} should work, with small changes in the proof, for any \(n\ge 1\)  and any general universal stability condition \(\phi \in V_{g,n}\) .. We believe that one advantage of our approach, with respect to the one of [1]}, is that the spaces \(\overline{J}^{trop}_{g,n}(\phi )\) , as \(\phi \)  varies in \(V_{g,n}\) , are constructed as generalized extended cone sub-complexes of \(\overline{J}^{trop}_{g,n}\) , which should be useful in order to study tropical wall-crossing phenomena (similar to [5]}).
